Question

The length and width of a rectangular patio are, (x + 7) feet and (x + 9) feet, respectively. If the area of the patio is 150 square feet, what are the dimensions of the patio? Enter the dimensions to two decimal places. The equation has real solution(s). The width (shorter dimension) of the patio is feet. The length (longer dimension) of the patio is feet.

Answer 1

Answer:

The width of the patio is 11.29 feet while the length of the patio is 13.29 feet

Step-by-step explanation:

Mathematically, the area of the patio can be calculated by multiplying the length by the breadth of the patio

Thus we have ;

(x + 7)(x + 9) = 150

x^2 + 7x + 9x + 63 = 150

x^2 + 16x + 63 = 150

x^2 + 16x + 63 -150 = 0

x^2 + 16x -87 = 0

we can use the quadratic formula to solve this completely

x = {-b ± √(b^2 - 4ac)}/2a

where a = 1, b = 16 and c = -87

Plugging the values we have

x = {-16 ± √(16^2 - 4(1)(-87)}/2

x = {-16 ± √(256+ 348)}/2

x = {-16 ± √(604}/2

x = (-16 + 24.58)/2 or (-16-24.58)/2

x = 4.29 or -20.29

Choosing x = -20.29 will make our dimensions negative, so we ignore it and make do with the positive value only

Thus our dimensions are 4.29 + 7 and 4.29 + 9

This is equal to 11.29 feet and 13.29 feet respectively